## Standard Gamble

A method of measuring health status (or some aspects of quality of life) using expected utility theory. It proceeds by asking an appropriate panel of judges to rank the entities to be measured. Any two of these are then assigned numbers that preserve their relative ordering (any numbers will do). A less preferred third entity is then offered each judge in uncertain combination with the more preferred entity and each is asked to say whether they prefer the uncertain prospect to the certainty of the less preferred of the initial two entities. The probability in the uncertain prospect is adjusted until the judge is indifferent between it and the certain prospect, at which point the judge will have implicitly assigned a numerical value to the third entity. In this way many entities can be measured on an interval scale (see Utility for an explanation of this). Thus, if H(.) denotes the index of health status, and three styles of living are ranked H(A) > H(B) > H(C), then letting H(A) = 4 and H(B) = 2, the value for H(C) can be found by adjusting p (the probability) until the following equation holds:

If, in an experiment, p = 0.4, then the values are H(A) = 4, H(B) = 2 and H(C) = 2/3. Of course, the set of values (H(C) and so on) obtained in this manner yields valuations of health states only if the subjects of the experiments are

326 Standardized Mortality Rate people who choose as though they are expected utility maximizers. See